Finite Group Databasebeta

← C2×#13115071 #15863783

Subgroups — C2×#13115071 #15863783

Order 3328.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719532C211yesmaximal, characteristic
2C2×#11718782C211yesmaximal, characteristic, complemented
3C2×#11718893C211yesmaximal, characteristic
4C2×#11718597C211yesmaximal, characteristic, complemented
5#13115071C218yesmaximal, direct product factor
6C2×#11718146C211yesmaximal, characteristic, complemented
7C2×#11718115C211yesmaximal, characteristic, complemented
8C22×C13×#104C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12#11719532—22no—
13#11719532—22no—
14#11719532—22no—
15#11719532C2214yes—
16C2×Q8×Dic13—21no—
17C2×D4×Dic13—21no—
18C2×D4×Dic13—22no—
19C2×#88180—21no—
20C2×#88180C2211yescharacteristic
21C22×C4⋊Dic13—21no—
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C2×C13×#104C418yescomplemented
26C2×C13×#104C2214yes—
27#11718893—22no—
28#11718893C2214yes—
29C2×#88075—21no—
30C2×#88072—21no—
31C2×#88071—22no—
32#11718782—22no—
33#11718782C2214yescomplemented
34C2×#88058—21no—
35C2×#88057—21no—
36#11718597—22no—
37#11718597C2214yescomplemented
38#11718146C2214yescomplemented
39#11718115C2214yescomplemented
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41—22no—
43C2×C13×#41—22no—
44C2×C13×#41C2×C414yes—
45C2×C13×#41D412yes—
46C2×C13×#41Q814yes—
47C2×C13×#41C2312yes—
48C22×Q8×C13D411yescharacteristic
49C22×D4×C13—21no—
50C22×D4×C13D411yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C23×C4×C13C2311yescharacteristic
54C23×Dic13—22no—
55C23×Dic13—21no—
56C23×Dic13D412yes—
57C2×C13×M16—21no—
58C2×C13×M16—22no—
59C2×C13×M16C2×C414yescomplemented
60C2×C13×M16C2312yes—
61C22×C8×C13—21no—
62C2×C42×C13—21no—
63C2×C42×C13—22no—
64C2×C42×C13C2×C414yescomplemented
65C2×C42×C13C2312yes—
66C2×C22⋊Dic13—22no—
67C2×C22⋊Dic13—21no—
68Q8×Dic13—24no—
69Q8×Dic13—24no—
70D4×Dic13—28no—
71D4×Dic13—24no—
72D4×Dic13—24no—
73D4×Dic13—28no—
74#88180—24no—
75#88180—21no—
76#88180—21no—
77#88180—24no—
78#88180D412yes—
79#88180C2312yes—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—24no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—24no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13D412yes—
93C2×C4⋊Dic13D411yescharacteristic
94C2×C4⋊Dic13D411yescharacteristic
95C2×C4⋊Dic13C2312yes—
96C2×C4⋊Dic13C2312yes—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—21no—
99C2×#6099—21no—
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099C2312yes—
103C22×#1055—21no—
104C13×#104C2×C4116yescomplemented
105#88075—24no—
106#88072—24no—
107#88071—28no—
108#88058—24no—
109#88057—24no—
110C2×#1860—131nomaximal, Sylow
111C24×C13—21no—
112C24×C13C2×D411yescharacteristic
113C13×#41—24no—
114C13×#41—24no—
115C13×#41—24no—
116C13×#41—24no—
117C13×#41—24no—
118C13×#41—22no—
119C13×#41—22no—
120C13×#41C4⋊C418yes—
121C13×#41C22×C414yes—
122C13×#41C2×Q814yes—
123C2×Q8×C13—21no—
124C2×Q8×C13—22no—
125C2×Q8×C13C4⋊C414yes—
126C2×Q8×C13C2×D412yes—
127C2×D4×C13—24no—
128C2×D4×C13—22no—
129C2×D4×C13—24no—
130C2×D4×C13—22no—
131C2×D4×C13—21no—
132C2×D4×C13—22no—
133C2×D4×C13C4⋊C414yes—
134C2×D4×C13C2×D412yes—
135C22×C4×C13—21no—
136C22×C4×C13—24no—
137C22×C4×C13—22no—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—24no—
141C22×C4×C13—22no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13C22×C412yes—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×Q812yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—22no—
156C22×Dic13—21no—
157C22×Dic13—28no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—44no—
161C22×Dic13—44no—
162C22×Dic13—41no—
163C22×Dic13—41no—
164C22×Dic13—84no—
165C22×Dic13C2×D414yes—
166C13×M16—24no—
167C13×M16—22no—
168C13×M16C22×C414yescomplemented
169C2×C8×C13—24no—
170C2×C8×C13—22no—
171C42×C13—24no—
172C42×C13—22no—
173C42×C13C22×C414yescomplemented
174C22⋊Dic13—28no—
175C22⋊Dic13—22no—
176C22⋊Dic13—22no—
177C4⋊Dic13—28no—
178C4⋊Dic13—22no—
179C4⋊Dic13—21no—
180C4⋊Dic13—22no—
181C4⋊Dic13—21no—
182C4⋊Dic13—22no—
183C4⋊Dic13—22no—
184C4⋊Dic13—22no—
185C4⋊Dic13—22no—
186C4⋊Dic13—41no—
187C4⋊Dic13—41no—
188C4⋊Dic13C2×D412yes—
189C4⋊Dic13C2×D412yes—
190C4×Dic13—28no—
191C4×Dic13—22no—
192C4×Dic13—22no—
193#6099—22no—
194#6099—22no—
195#6099—42no—
196C2×#1055—22no—
197C2×#1055—42no—
198C2×#520—131no—
199C2×#428—131no—
200C22×#104D1311yescharacteristic
201C2×#417—131no—
202C2×#382—131no—
203#1860—138no—
204C2×#343—131no—
205C2×#339—131no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—24no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13C4×D412yes—
213C23×C13#12011yescharacteristic
214C23×C13#12011yescharacteristic
215C23×C13C22⋊Q812yes—
216C23×C13C22×D411yescharacteristic
217Q8×C13—22no—
218Q8×C13—24no—
219Q8×C13C2×C4⋊C414yes—
220D4×C13—24no—
221D4×C13—24no—
222D4×C13—28no—
223D4×C13—22no—
224D4×C13—24no—
225D4×C13C2×C4⋊C414yes—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—28no—
231C2×C4×C13—24no—
232C2×C4×C13—48no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13C2×C4⋊C412yes—
236C2×C4×C13C2×C4⋊C412yes—
237C2×C4×C13C4×D412yes—
238C2×C4×C13C4×D412yes—
239C2×C4×C13C4×D412yes—
240C2×C4×C13#12011yescharacteristic
241C2×C4×C13#12011yescharacteristic
242C2×C4×C13C22⋊Q812yes—
243C2×C4×C13C22⋊Q812yes—
244C2×C4×C13C22⋊Q812yes—
245C2×C4×C13#12312yes—
246C2×C4×C13#12312yes—
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×Q811yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—22no—
256C2×Dic13—42no—
257C2×Dic13—44no—
258C2×Dic13—42no—
259C2×Dic13—44no—
260C2×Dic13—44no—
261C2×Dic13—42no—
262C2×Dic13—82no—
263C2×Dic13—88no—
264C2×Dic13—82no—
265C2×Dic13—82no—
266C8×C13—24no—
267#1055—42no—
268C22×#41C2×D1311yescharacteristic
269C22×M16—131no—
270C22×M16C2×D1311yescharacteristic
271#520—134no—
272#520—262no—
273#520—262no—
274#520—262no—
275C2×C4×Q8—261no—
276C2×C4×D4—262no—
277C2×C4×D4—261no—
278C2×#117—131no—
279C2×#117—261no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4—261no—
283C22×C42C2×D1311yescharacteristic
284#428—134no—
285#428—262no—
286C2×#107—261no—
287C2×#106—261no—
288C2×#104Dic1318yescomplemented
289C2×#104C2×D1314yes—
290#417—134no—
291#417—262no—
292C2×#103—261no—
293C2×#102—261no—
294#382—134no—
295#382—262no—
296C2×#95—262no—
297#343—134no—
298#339—134no—
299C22×C13—24no—
300C22×C13—24no—
301C22×C13—21no—
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13—24no—
306C22×C13—48no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13#38512yes—
310C22×C13#38512yes—
311C22×C13#45412yes—
312C22×C13#45512yes—
313C22×C13C2×C4×D411yescharacteristic
314C22×C13C2×#12011yescharacteristic
315C22×C13C2×C22⋊Q811yescharacteristic
316C4×C13—24no—
317C4×C13—44no—
318C4×C13#38512yes—
319C4×C13#38512yes—
320C4×C13C22×C4⋊C411yescharacteristic
321C4×C13C2×C4×D411yescharacteristic
322C4×C13C2×C22⋊Q811yescharacteristic
323C4×C13C2×#12311yescharacteristic
324Dic13—44no—
325Dic13—42no—
326Dic13—42no—
327Dic13—82no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41Dic2614yes—
333C2×#41D5212yes—
334C2×#41C2×Dic1314yes—
335C2×#41C22×D1312yes—
336C22×Q8D5211yescharacteristic
337C22×D4—21no—
338C22×D4D5211yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—132no—
342C23×C4—262no—
343C23×C4—261no—
344C23×C4C22×D1311yescharacteristic
345C2×M16—21no—
346C2×M16—22no—
347C2×M16—132no—
348C2×M16—261no—
349C2×M16—262no—
350C2×M16—262no—
351C2×M16C2×Dic1314yescomplemented
352C2×M16C22×D1312yes—
353C22×C8—21no—
354C22×C8—261no—
355C4×Q8—264no—
356C4×Q8—264no—
357C4×D4—268no—
358C4×D4—268no—
359C4×D4—264no—
360C4×D4—264no—
361#117—132no—
362#117—132no—
363#117—264no—
364#117—264no—
365#117—261no—
366#117—261no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—132no—
370C2×C4⋊C4—132no—
371C2×C4⋊C4—132no—
372C2×C4⋊C4—264no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—264no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C22⋊C4—262no—
385C2×C22⋊C4—261no—
386C2×C42—21no—
387C2×C42—22no—
388C2×C42—262no—
389C2×C42—261no—
390C2×C42C2×Dic1314yescomplemented
391C2×C42C22×D1312yes—
392#107—264no—
393#106—264no—
394#104C2×Dic13116yescomplemented
395#103—264no—
396#102—264no—
397#95—268no—
398C2×C13—21no—
399C2×C13—21no—
400C2×C13—22no—
401C2×C13—44no—
402C2×C13#186014yescomplemented
403C2×C13C2×#38511yescharacteristic
404C2×C13C2×#45511yescharacteristic
405C2×C13C2×#45411yescharacteristic
406C24—21no—
407C24D4×D1311yescharacteristic
408#41—24no—
409#41—24no—
410#41—24no—
411#41—24no—
412#41—24no—
413#41—22no—
414#41—22no—
415#41C4⋊Dic1318yes—
416#41C2×Dic2614yes—
417#41C22×Dic1314yes—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8C4⋊Dic1314yes—
421C2×Q8C2×D5212yes—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—24no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4C4⋊Dic1314yes—
429C2×D4C2×D5212yes—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—134no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—262no—
443C22×C4—268no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—524no—
447C22×C4—524no—
448C22×C4—521no—
449C22×C4—521no—
450C22×C4—1044no—
451C22×C4C2×Dic2612yes—
452C22×C4C2×D5211yescharacteristic
453C22×C4C2×D5211yescharacteristic
454C22×C4D4×D1311yescharacteristic
455C22×C4D4×D1311yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4#612912yes—
458C22×C4#612912yes—
459C22×C4C22×Dic1312yes—
460C22×C4C23×D1311yescharacteristic
461M16—24no—
462M16—22no—
463M16—262no—
464M16—262no—
465M16—522no—
466M16C22×Dic1314yescomplemented
467C2×C8—24no—
468C2×C8—22no—
469C2×C8—262no—
470C2×C8—522no—
471C4⋊C4—132no—
472C4⋊C4—132no—
473C4⋊C4—268no—
474C4⋊C4—261no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C4⋊C4—261no—
478C4⋊C4—262no—
479C4⋊C4—262no—
480C4⋊C4—262no—
481C4⋊C4—262no—
482C4⋊C4—521no—
483C4⋊C4—521no—
484C22⋊C4—268no—
485C22⋊C4—262no—
486C22⋊C4—262no—
487C42—24no—
488C42—22no—
489C42—268no—
490C42—262no—
491C42—262no—
492C42C22×Dic1314yescomplemented
493C13C2×#186011yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—24no—
498C23—42no—
499C23—42no—
500C23#8813212yes—
501C23#8813611yescharacteristic
502C23#8813611yescharacteristic
503C23D4×Dic1312yes—
504C23C2×D4×D1311yescharacteristic
505Q8—22no—
506Q8—24no—
507Q8C2×C4⋊Dic1314yes—
508D4—24no—
509D4—24no—
510D4—28no—
511D4—22no—
512D4—24no—
513D4C2×C4⋊Dic1314yes—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—28no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—48no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—264no—
526C2×C4—524no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—524no—
530C2×C4—524no—
531C2×C4—522no—
532C2×C4—1042no—
533C2×C4—1048no—
534C2×C4—1042no—
535C2×C4—1042no—
536C2×C4#8813212yes—
537C2×C4#8813212yes—
538C2×C4#8813212yes—
539C2×C4#8813611yescharacteristic
540C2×C4#8813611yescharacteristic
541C2×C4#8814012yes—
542C2×C4#8814012yes—
543C2×C4C2×C4⋊Dic1312yes—
544C2×C4C2×C4⋊Dic1312yes—
545C2×C4D4×Dic1312yes—
546C2×C4D4×Dic1312yes—
547C2×C4D4×Dic1312yes—
548C2×C4C22×Dic2611yescharacteristic
549C2×C4C22×D5211yescharacteristic
550C2×C4C2×D4×D1311yescharacteristic
551C2×C4C2×#612911yescharacteristic
552C2×C4C2×#612911yescharacteristic
553C2×C4C23×Dic1311yescharacteristic
554C8—24no—
555C8—522no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—48no—
566C22#1171848612yes—
567C22#1171848812yes—
568C22#1171861112yes—
569C22#1171861112yes—
570C22C2×#8813211yescharacteristic
571C22C2×#8813611yescharacteristic
572C22C2×D4×Dic1311yescharacteristic
573C4—24no—
574C4—44no—
575C4—524no—
576C4—522no—
577C4—522no—
578C4—1042no—
579C4#1171861112yes—
580C4#1171861112yes—
581C4C2×#8813211yescharacteristic
582C4C2×#8814011yescharacteristic
583C4C22×C4⋊Dic1311yescharacteristic
584C4C2×D4×Dic1311yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—44no—
589C2#1311507114yesdirect product factor
590C2C2×#1171861111yescharacteristic
591C2C2×#1171848611yescharacteristic
592C2C2×#1171848811yescharacteristic
subgroupG/H
centerC23#88136
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#104C2
socleC23×C13#120
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC22×#104D13
hypocenterC13C2×#1860
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#11718782C2semidirect
4. C2×#11718597C2semidirect
5. #13115071C2direct (N × H)
6. C2×#11718146C2semidirect
7. C2×#11718115C2semidirect
25. C2×C13×#104C4semidirect
33. #11718782C22semidirect
37. #11718597C22semidirect
38. #11718146C22semidirect
39. #11718115C22semidirect
59. C2×C13×M16C2×C4semidirect
64. C2×C42×C13C2×C4semidirect
104. C13×#104C2×C4semidirect
168. C13×M16C22×C4semidirect
173. C42×C13C22×C4semidirect
288. C2×#104Dic13semidirect
351. C2×M16C2×Dic13semidirect
390. C2×C42C2×Dic13semidirect
394. #104C2×Dic13semidirect
402. C2×C13#1860semidirect
466. M16C22×Dic13semidirect
492. C42C22×Dic13semidirect
493. C13C2×#1860semidirect
589. C2#13115071direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117195322
C2×#117187822
C2×#117188932
C2×#117185972
#131150712
C2×#117181462
C2×#117181152
C22×C13×#1042
C2×#186013